SPL function of speed or acceleration

[gary f]

Hello Mathematicians out there.

Is Sound Pressure Level generated by a transducer proportional to speed of the cone or acceleration of the cone.

F

[DanWiggins]

Acceleration of the cone. This is why the velocity doubles as you drop an octave, and the displacement quadruples as you drop an octave (assuming the SPL level stays the same).

Dan Wiggins
Adire Audio

[gary f]

Thanks Dan,

I wonder, I saw the parthenon driver used as a dipole driver. How come the front pressure wave and rear pressure wave don't cancel each other?

F

[454Casull]

They do if the Parthenon isn't put into an enclosure.

[Svante]

Originally posted by gary f
Hello Mathematicians out there.

Is Sound Pressure Level generated by a transducer proportional to speed of the cone or acceleration of the cone.

F

If mounted in a box it is proportional to the acceleration.

The pressure from a point source is:

p=(U*rho0*w)/(4*pi*r)

where U is the volume flow (m3/s), rho0 is the density of air (=1.2 m3/s), w is the angular frequency (rad/s), r is the distance. Free field conditions are assumed. For low frequencies, a loudspeaker can be approcimated by a point source, and volume flow U is:

U=Sd*v

where Sd is the equivalent piston area of the speaker, and v is the velocity of the cone.

So p is oproportional to w*v which in turn is equal to the acceleration (with a 90 degree phase shift).

[DanWiggins]

Originally posted by gary f
Thanks Dan,

I wonder, I saw the parthenon driver used as a dipole driver. How come the front pressure wave and rear pressure wave don't cancel each other?

F

They do cancel, as a dipole speaker should. With a baffle width of 24", it will start cancellation around 280 Hz, and roll off at 6 dB/octave below that. Of course, with so much displacement to start with, you can still do 110+ dB @ 20 Hz...

The concept was not only to make the wildest looking driver you've ever seen, but one with so much potential output that it's kind of a "so what" in terms of loss. There's so much to start with, you don't NEED a box.

Dan Wiggins
Adire Audio

[JMB]

Based on your equations, it appears, then, that a more efficient or louder speaker of equal Sd would have a better transient response. Is this correct?

[bhg41088]

is there a video of that thing going at it?

[roddyama]

Originally posted by gary f
Hello Mathematicians out there.

Is Sound Pressure Level generated by a transducer proportional to speed of the cone or acceleration of the cone.

F

OK, here we go.

Sound pressure is proportional to the cone velocity.

Two examples, one real and one conceptual.

1.) A jet plane has broken the sound barrier and is now traveling at a constant speed of mach 1.X. The "sonic boom" is a sonic pressure wave created by the plane traveling at a contasnt velocity. The planes acceleration is zero.

2.) A speaker cone is driven by a triangle wave signal and the cone follows the signal perfectly. The cone moves at a constant velocity and changes direction instantaneously at the ends of its travel. Sound pressure will be generated by the movement of the cone and the SPL will be proportional to the cones velocity. If the SPL were proportional to the acceleration, the SPL would be infinite.

[sreten]

Originally posted by JMB
Based on your equations, it appears, then, that a more efficient or louder speaker of equal Sd would have a better transient response. Is this correct?

A very fallacious assumption.

A bit like amplifier slew rate requirements - which is faster :

a) a 10W 10V/us amplifier or
b) a 100W 20V/us amplifier ?

some would say b) by definition, but IMO its a).

sreten.